This paper presents a finite element method for solving the neutron transport equation, which is a first-order hyperbolic partial differential equation. The authors start by introducing a discontinuous Galerkin method for ordinary differential equations, which is shown to be strongly A-stable and of order \(2k+1\). This method is then generalized to the two-dimensional neutron transport problem. The finite element approximation is derived, and error bounds in the \(L^2\)-norm are established. The paper also discusses a superconvergence result, showing that the rate of convergence of the finite element method is \(O(h^{k+1})\) when all elements are rectangles and the polynomial degree is \(k\). The theoretical results are supported by numerical calculations, which suggest that even more precise error bounds may hold at certain points on the boundary of the elements.This paper presents a finite element method for solving the neutron transport equation, which is a first-order hyperbolic partial differential equation. The authors start by introducing a discontinuous Galerkin method for ordinary differential equations, which is shown to be strongly A-stable and of order \(2k+1\). This method is then generalized to the two-dimensional neutron transport problem. The finite element approximation is derived, and error bounds in the \(L^2\)-norm are established. The paper also discusses a superconvergence result, showing that the rate of convergence of the finite element method is \(O(h^{k+1})\) when all elements are rectangles and the polynomial degree is \(k\). The theoretical results are supported by numerical calculations, which suggest that even more precise error bounds may hold at certain points on the boundary of the elements.